dask.array.random.standard_gamma
dask.array.random.standard_gamma¶
- dask.array.random.standard_gamma(shape, size=None, chunks='auto', **kwargs)¶
Draw samples from a standard Gamma distribution.
This docstring was copied from numpy.random.mtrand.RandomState.standard_gamma.
Some inconsistencies with the Dask version may exist.
Samples are drawn from a Gamma distribution with specified parameters, shape (sometimes designated “k”) and scale=1.
Note
New code should use the
standard_gamma
method of adefault_rng()
instance instead; please see the Quick Start.- Parameters
- shapefloat or array_like of floats
Parameter, must be non-negative.
- sizeint or tuple of ints, optional
Output shape. If the given shape is, e.g.,
(m, n, k)
, thenm * n * k
samples are drawn. If size isNone
(default), a single value is returned ifshape
is a scalar. Otherwise,np.array(shape).size
samples are drawn.
- Returns
- outndarray or scalar
Drawn samples from the parameterized standard gamma distribution.
See also
scipy.stats.gamma
probability density function, distribution or cumulative density function, etc.
Generator.standard_gamma
which should be used for new code.
Notes
The probability density for the Gamma distribution is
\[p(x) = x^{k-1}\frac{e^{-x/\theta}}{\theta^k\Gamma(k)},\]where \(k\) is the shape and \(\theta\) the scale, and \(\Gamma\) is the Gamma function.
The Gamma distribution is often used to model the times to failure of electronic components, and arises naturally in processes for which the waiting times between Poisson distributed events are relevant.
References
- 1
Weisstein, Eric W. “Gamma Distribution.” From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/GammaDistribution.html
- 2
Wikipedia, “Gamma distribution”, https://en.wikipedia.org/wiki/Gamma_distribution
Examples
Draw samples from the distribution:
>>> shape, scale = 2., 1. # mean and width >>> s = np.random.standard_gamma(shape, 1000000)
Display the histogram of the samples, along with the probability density function:
>>> import matplotlib.pyplot as plt >>> import scipy.special as sps >>> count, bins, ignored = plt.hist(s, 50, density=True) >>> y = bins**(shape-1) * ((np.exp(-bins/scale))/ ... (sps.gamma(shape) * scale**shape)) >>> plt.plot(bins, y, linewidth=2, color='r') >>> plt.show()